AFM Homework Name Directions: a)Determine if the graph is ... · AFM Homework 4-7 Writing Piecewise...
Transcript of AFM Homework Name Directions: a)Determine if the graph is ... · AFM Homework 4-7 Writing Piecewise...
AFM Homework Name___________________________ 4-1 Functions Date_____________ Period _______
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Directions: a)Determine if the graph is a function b) Find the domain and range of the graph
c) Identify where the graph is increasing/decreasing/constant 1. 2.
Dec: ________
3. 4.
5. 6.
Function: _____________ Domain: ______________ Range: ________________ Inc: ____________________ Dec: ___________________ Con: ____________________
Function: _____________ Domain: ______________ Range: ________________ Inc: ____________________ Dec: ___________________ Con: ____________________
Function: _____________ Domain: ______________ Range: ________________ Inc: ____________________ Dec: ___________________ Con: ____________________
Function: _____________ Domain: ______________ Range: ________________ Inc: ____________________ Dec: ___________________ Con: ____________________
Function: _____________ Domain: ______________ Range: ________________ Inc: ____________________ Dec: ___________________ Con: ____________________
Function: _____________ Domain: ______________ Range: ________________ Inc: ____________________ Dec: ___________________ Con: ____________________
AFM Homework 4-1 Functions
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7. 8.
9. 10.
Function: _____________ Domain: ______________ Range: ________________ Inc: ____________________ Dec: ___________________ Con: ____________________
Function: _____________ Domain: ______________ Range: ________________ Inc: ____________________ Dec: ___________________ Con: ____________________
Function: _____________ Domain: ______________ Range: ________________ Inc: ____________________ Dec: ___________________ Con: ____________________
Function: _____________ Domain: ______________ Range: ________________ Inc: ____________________ Dec: ___________________ Con: ____________________
AFM Homework Name___________________________ 4-2 Finding Domain w/o a Graph Date_____________ Period _______
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Find the domain of given functions.
1. ! ! = !! + 1
2. ! ! = 5
3. ! ! = !
!!!
4. ! ! = !!
5. ! ! = !!!!!
6. ! ! = !!!
!!!!
7. ! ! = !! + 2! − 8
8. ! ! = !!!!
9. ℎ ! = !!!!
!!!!
10. ! ! = ! + 4
11. ! ! = !!!
!!!
12. ! ! = !! + 4! − 5
13. ! ! = !!!
!!!
14. ! ! = 8 − 2!
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Worksheet by Kuta Software LLC
AFM
Homework 4-3
Name___________________________________ ID: 1
Date________________ Period____
Evaluate each function.
1) h(a) = a2 + 2; Find h(−9) 2) w(a) = −4a + 2; Find w(8)
3) p(x) = x2 − 5; Find p(8) 4) f (n) = 2n2; Find f (−9)
5) h(t) = −2 3t − 1 ; Find h(10) 6) k(t) = 2t ; Find k(−10)
7) h(x) = x3 − 4x; Find h(2 − x) 8) g(x) = 4x − 4; Find g(x2)
9) g(n) = 2n + 5; Find g(n + 2) 10) h(n) = −n2 − 1; Find h(4n)
11) p(t) = t2 − 2t; Find p(t − 1) 12) h(a) = −a2 − 4; Find h(1 − a)
AFM Homework Name___________________________ 4-4 Parent Function Discovery Date_____________ Period _______
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# 1- 6 Give the name of the parent function and describe the transformation represented. Sketch a graph of the parent function and the new function. 1. g(x) = x 2 – 1 Name: _________________________________________
Transformation:______________________________
2. f(x) = 2 1x− - 3 Name: _________________________________________
Transformation:______________________________
3. h(x) = - 2x− Name: _________________________________________
Transformation:______________________________
4. g(x) = -x3+ 3 Name: _________________________________________
Transformation:______________________________
AFM Homework 4-4 Parent Functions
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5. f(x) = 5x + - 2 Name: _________________________________________
Transformation:______________________________
#6-8 Identify the domain and range of the function. Describe the transformation from its parent function.
6. g(x) = x + 5 Domain : ______________________ Range : __________________
Transformations:___________________________________________ 7. h(x) = - x2 + 1 Domain : ______________________ Range : __________________
Transformations:___________________________________________ 8. h(x) = 2x− − Domain : ______________________ Range : __________________
Transformations:___________________________________________
AFM Homework Name___________________________ 4-5 Functions Date_____________ Period _______
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Drawtheparentfunctionusingadotted(---)line.Thensketchthefinalgraphusingasolid(-----)line.Describeeachtransformationandidentifythedomainandrangeofthefinalgraph.
1. ! ! = 2!! + 3
2. ! ! = 3− ! + 1
3. ! ! = − !! ! + 3
4. ! ! = − !! + 1 − 2
ParentFunction:________________________________Transformation:______________________________________________________________________________________Domain:___________________________________________Range:____________________________________________
ParentFunction:________________________________Transformation:______________________________________________________________________________________Domain:___________________________________________Range:____________________________________________
ParentFunction:________________________________Transformation:______________________________________________________________________________________Domain:___________________________________________Range:____________________________________________
ParentFunction:________________________________Transformation:______________________________________________________________________________________Domain:___________________________________________Range:____________________________________________
AFMHomework 4-5Transformations
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5. ! ! = !! !
! − 4
6. ! = 4+ ! − 1
ParentFunction:________________________________Transformation:______________________________________________________________________________________Domain:___________________________________________Range:____________________________________________
ParentFunction:________________________________Transformation:______________________________________________________________________________________Domain:___________________________________________Range:____________________________________________
Algebra 2 YL Name 4.4 Graphing Piecewise Functions Worksheet Date Period
1. 𝑓(𝑥) = −𝑥 if 𝑥 ≤ 2 𝑥 if 𝑥 > 2
� 2. 𝑓(𝑥) = 2, 𝑥 > −3−5, 𝑥 < −3
�
3. 𝑓(𝑥) = −1, 𝑥 ≤ −2 2, 𝑥 > −2
� 4. 𝑓(𝑥) = −1, 1, 𝑥,
� 𝑥 ≤ −1
−1 < 𝑥 < 1𝑥 > 1
5. 𝑓(𝑥) =−𝑥 + 2, 𝑥 ≤ 0
𝑥 + 3, 𝑥 > 0� 6. 𝑓(𝑥) =𝑥 + 2, 𝑥 ≤ 2
− 𝑥 + 4, 𝑥 > 2�
7. 𝑓(𝑥) = −3𝑥 − 4, 𝑥 ≤ −2𝑥 + 1, 𝑥 > −2
� 8. 𝑓(𝑥) = −𝑥, 𝑥 ≤ 02𝑥 − 2, 𝑥 > 0
�
9. 𝑓(𝑥) = −𝑥 − 4, − 𝑥, −1,
� 𝑥 < −2
−2 ≤ 𝑥 ≤ 2𝑥 > 2
10. 𝑓(𝑥) = 3, 𝑥 < −1𝑥 + 1, 1 ≤ 𝑥 ≤ 4
�
11. 𝑓(𝑥) = 𝑥 − 1, 𝑥 ≠ 43, 𝑥 = 4
� 12. 𝑓(𝑥) = 𝑥 + 4, − 6,−𝑥 + 2,
� −6 ≤ 𝑥 < 2
𝑥 = 2𝑥 > 2
2.8.3 Piecewise Function Worksheet Page 1
Integrated 3 Unit 2 Name 2.8.3 Piecewise Function Worksheet
For problems 1-12, evaluate the function for the given values of x.
>
≤=
0,20,3
)(xifxif
xf
>−
≤+=
3,123,5
)(xxxx
xg
−>−
−≤−=
2,23
2,421
)(xx
xxxh
1. f(2) 2. f (-4) 3. f (0) 4. f (½)
5. g(7) 6. g (0) 7. g (-1) 8. g (3)
9. h(-4) 10. h (-2) 11. h (-1) 12. h (6)
Graph the function.
13.
>+
≤−=
1,131,32
)(xwhenxxwhenx
xf 14.
≥+
<−=
2,122,1
)(xwhenxxwhenx
xf
Match the piecewise function with its graph.
15.
>
≤−=
1,31,4
)(xxxx
xf 16.
>+
≤+=
0420,4
)(xxxx
xf 17.
>+
≤−=
1,21,23
)(xxxx
xf
18.
<+
≥==
0,40,32
)(xxxx
xf 19.
−<−
−≥−=
1,51,13
)(xxx
xf 20.
>−
≤−−=
1,51,13
)(xxx
xf
2.8.3 Piecewise Function Worksheet Page 2
Write the function for the given graphs.
21. 22.
23. Graph the step function.
<≤−
−<≤−=
21,314,1
)(xwhenxwhen
xf
24. Write the step function.
25. You have a summer job that pays time and half for overtime. That means, if you work more than 40
hours in a week, your hourly wage for the extra hours in 1.5 times your normal rate of $7 per hour. a. Write a piecewise function describing your weekly pay, P in term of the number of hours
worked, h. b. How much will you get paid if you work 47 hours? c. How much will you get paid if you work 30 hours?
AFM Homework Name___________________________
4-8 Application of Piecewise Functions Date_____________ Period _______
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1. You are a buyer for a grocery store and you are asked to purchase potatoes for the
grocery store. The distributor of potatoes tells you that if you buy up to 50 bushels
of potatoes, you will pay $40 per bushel; and for each bushel you purchase above 50
bushels, you will pay $30 per bushel.
a. How much will your grocery store pay in total if you decide to purchase 40
bushels? 60 bushels? 100 bushels?
b. Write a function which has as its input values (x-values) the number of
bushels of potatoes purchased and outputs the total amount of money that
your grocery store will pay for the potatoes.
2. A certain country taxes the first $20,000 of an individual’s income at a rate of 15%,
and all income over $20,000 is taxed at 20%.
a. Al makes $16,000. Betty makes $36,000. How much is each taxed?
b. Write a piecewise function T that specifies the total tax on an income of x
dollars.
c. Catina is taxed $5000. What is her income?
AFM Homework 4-8 Application of Piecewise Functions
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3. A museum charges $40 for a group of 10 or fewer people. A group of more than 10 people must, in addition to the $40, pay $2 per person for the number of people above 10. For example, a group of 12 pays $44 and a group of 15 pays $50. The maximum group size is 50.
a. Find a function, C = f(x), that represents the cost as a function of the number of
people going to the museum.
b. How much would the museum charge for a group of 8? Group with 35 people?